The American Cancer Society estimates that 20,500 tumors of the brain or nervous system will be diagnosed during 2007 in the United States, and approximately 12,740 people will die from these tumors, and high grade-grade gliomas (glioblastoma multiforme, anaplastic astrocytoma and oligo-astrocytoma) are the most lethal forms of primary brain tumors. It has been reported that in the US, approximately 40% of all primary brain tumors and 78% of all malignant brain tumors are gliomas. Novel therapies, which can directly and selectively attack infiltrating tumor cells while sparing normal tissue, are desperately needed in malignant glioma therapy. TM601 binds with high affinity to tumor cells through a receptor expressed on the surface of tumor cells, but not on the surface of normal cells. TM601 has been found to pass the blood brain barrier and some clinical evidence of tumor response in early imaging studies and data from non-clinical studies suggests that the peptide is an active angiogenesis inhibitor. This Phase 1 study will evaluate the safety and the target recommended Phase 2 dose of TM601 in patients with recurrent malignant glioma who have failed first-line, standard therapy. Anti-tumor effects will be determined by secondary efficacy measures through perfusion MRI imaging. Patients will be assigned to each dose level in groups of three, with escalation to the next highest dose, dependent upon demonstrated tolerance in the previous dosing group, until either a maximum tolerated dose (MTD) is defined or perfusion changes have been demonstrated in five out of six patients in a cohort. Patients will be administered an imaging dose of 131I-TM601 by intravenous (IV) infusion to demonstrate tumor specific localization. Only patients demonstrating tumor specific uptake of 131I-TM601 on a brain SPECT scan will remain on study to receive treatment with non-labeled TM601. One week after the imaging dose, study patients will receive non-labeled TM601 by IV infusion at one of six dose levels once a week for 3 weeks. Subsequent cycles of non-labeled TM601 will be administered as long as there is no evidence of disease progression and the patient experiences no dose-limiting toxicities (DLTs). Clinical response to TM601 will be assessed in each study patient at the completion of each cycle and at study completion, 28 days post final TM601 dose. The highest active dose will be studied in Phase 2 in this population.